Abstract: Quantum synchronizable codes are quantum error correcting codes that can correct not only Pauli errors but also errors in block synchronization. The code can be constructed from two classical cyclic codes C, D satisfying C⊥⊂C⊂D through the Calderbank-Shor-Steane (CSS) code construction. In this work, we establish connections between quantum synchronizable codes, subsystem codes, and […]
Abstract: Quantum sensing holds great promise for high-precision magnetic field measurements. However, its performance is significantly limited by noise. The investigation of active quantum error correction to address this noise led to the Hamiltonian-not-in-Lindblad-span (HNLS) condition. This states that the Heisenberg scaling is achievable if and only if the signal Hamiltonian is orthogonal to the […]
Abstract: In this article, we consider second-generation (2G) quantum repeaters (QRs) for creating long-distance entanglement in quantum networks. Combining a distance-dependent depolarizing error model with the nonlocal Bell state purification procedure required by 2G QRs leads to an error model consisting of correlated and biased errors. To correct correlated errors, nonsymmetric Calderbank–Steane–Shor (CSS) codes with […]
Abstract: This article proposes a novel low-complexity syndrome-based linear programming (SB-LP) decoding algorithm for decoding quantum low-density parity-check codes. Under the code-capacity model, the SB-LP decoder can be used as a standalone decoder; however, it is particularly powerful when used as a postprocessing step following SB min-sum (SB-MS) decoding. In the latter case, the proposed […]
Abstract: Neutral atom arrays manipulated with optical tweezers are promising candidates for fault-tolerant quantum computers due to their advantageous properties, such as scalability, long coherence times, and optical accessibility for communication. A significant challenge to overcome is the presence of non-Pauli errors, specifically erasure errors and leakage errors. Previous work has shown that leakage errors […]
Abstract: Reaching fault-tolerant quantum computation relies on the successful implementation of non-Clifford circuits with quantum error correction (QEC). In QEC, quantum gates and measurements encode quantum information into an error-protected Hilbert space, while classical processing decodes the measurements into logical errors. QEC non-Clifford gates pose the greatest computation challenge from the classical controller’s perspective, as […]
Abstract: Quantum error correction is crucial for universal fault-tolerant quantum computing. Highly accurate and low-time-complexity decoding algorithms play an indispensable role in ensuring quantum error correction works effectively. Among existing decoding algorithms, belief propagation (BP) is notable for its nearly linear time complexity and general applicability to stabilizer codes. However, BP’s decoding accuracy without postprocessing […]
Abstract: Given that quantum error correction processes are unreliable, an efficient error syndrome extraction circuit should use fewer ancillary qubits, quantum gates, and measurements while maintaining low circuit depth, to minimize the circuit area, roughly defined as the product of circuit depth and the number of physical qubits. We propose to design parallel flagged syndrome […]
Quantum error correction and the use of quantum error correction codes are likely to be essential for the realization of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes that are tailored for a particular error model may have much better performance. For more about this article see link below. […]
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints and are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial optimization remains an ongoing area of study. Here, we propose new methods for producing approximate solutions to quadratic unconstrained binary optimization problems, […]